In ion implantation for forming source and drain regions of a MOS transistor, implanted impurities collide with atoms constituting the substrate, diffuse in a lateral direction and distribute below a gate electrode. As the gate length becomes short, an impurity concentration distribution in a lateral direction influences the device performance greatly. It is therefore important to know an impurity concentration distribution in a lateral direction in the region below a gate electrode. It is, however, difficult to directly measure an impurity concentration distribution in a lateral direction.
A method of evaluating an impurity concentration distribution in a lateral direction is described (for example, refer to the paper “Estimating lateral straggling of impurity profiles of ions implanted into crystalline silicon” by K. Suzuki, R. Sudo, and M. Nagase, IEEE Trans. Electron Devices, ED-48, pp. 2803-2807, 2001).
An xy orthogonal coordinate system and an st orthogonal coordinate system are defined as shown in FIG. 1. The origins of both the systems are coincident, and positioned on the surface of a semiconductor substrate. A y-axis is parallel to a propagation direction of an ion beam of ion implantation, and an s-axis is perpendicular to the surface of the semiconductor substrate. Both the positive sense of each of the y-axis and s-axis looks toward the inside of the substrate. When the angle of incidence of the ion beam is θ, an angle between the y-axis and s-axis is equal to θ.
An x-axis and a t-axis are disposed on a plane on which the y-axis and s-axis are disposed. The positive sense of the x-axis looks toward the inside of the substrate. The t-axis is contained in the surface of the semiconductor substrate, and the positive sense of the t-axis looks toward upstream of an ion beam.
An impurity concentration distribution formed by an ion beam incident upon the origin is defined by D(x, y). An impurity concentration distribution formed by an ion beam incident upon a position x=u is expressed by D(x−u, y+u×tan θ).
An impurity concentration distribution dN(x, y) at a coordinate point (x, y) formed by an ion beam incident upon a position between x=u and x=u+du is given by the following formula (1):dN(x,y)=D(x−u,y+u tan θ)du 
If ion implantation is performed by assuming that the surface area of a semiconductor substrate is infinite and the whole area in a direction of the x-axis is scanned with an ion beam, an impurity concentration N(x, y) at the coordinate point (x, y) is given by the following formula (2):
      N    ⁡          (              x        ,        y            )        =            ∫              -        ∞            ∞        ⁢                  D        ⁡                  (                                    x              -              u                        ,                          y              +                              u                ⁢                                                                  ⁢                tan                ⁢                                                                  ⁢                θ                                              )                    ⁢                          ⁢              ⅆ        u            
The coordinates (x, y) and (s, t) have the relation given by the following formulas (3):x=t cos θ+s sin θy=s cos θ−t sin θ
The impurity concentration N(s, t) at the coordinate point (s, t) is therefore given by the following formula (4):
      N    ⁡          (              s        ,        t            )        =            ∫              -        ∞            ∞        ⁢                  D        ⁡                  (                                                    t                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                θ                            +                              s                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                θ                            -              u                        ,                                          s                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                θ                            -                              t                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                θ                            +                              u                ⁢                                                                  ⁢                tan                ⁢                                                                  ⁢                θ                                              )                    ⁢                          ⁢              ⅆ        u            
Since the impurity concentration is supposed not to depend on t, a dummy variable k given by the following formula (5) is defined in order to eliminate the variable t from the formula (4):
  k  =                              -          t                ⁢                                  ⁢        sin        ⁢                                  ⁢        θ            +              u        ⁢                                  ⁢        tan        ⁢                                  ⁢        θ                    tan      ⁢                          ⁢      θ      
The formula (4) is rewritten by using the variable k to obtain the following formula (6):
      N    ⁡          (      s      )        =            ∫              -        ∞            ∞        ⁢                  D        ⁡                  (                                                    s                ⁢                                                                  ⁢                sin                ⁢                                                                  ⁢                θ                            -              u                        ,                                          s                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                θ                            +                              u                ⁢                                                                  ⁢                tan                ⁢                                                                  ⁢                θ                                              )                    ⁢                          ⁢              ⅆ        u            
If y<0, D(x, y)=0. It is therefore sufficient that integration in the formula (6) is performed only in the region given by the following formula (7):s cos θ+u tan θ≧0
Therefore, a lower limit value of the integration range of the formula (6) may be set to:
  -      s    ⁡          (                        cos          ⁢                                          ⁢          θ                          tan          ⁢                                          ⁢          θ                    )      
Consider now the case in which an impurity concentration distribution D(x, y) is expressed by a product of a function n(y) dependent upon only a depth direction y and a function g(x, y) dependent upon also a lateral direction x. It is assumed that the functions n(y) and g(x, y) are normalized by a dose. A well-known dual Pearson IV distribution may be adopted as a normalized impurity concentration distribution n(y) in a depth direction. It is also possible to adopt a distribution described in the paper “Analytical expression for ion-implanted impurity concentration profiles”, by K. Suzuki and R. Sudo, Solid-State Electronics, vol. 44, pp. 2253-2257, 2001. A normalized impurity concentration distribution g(x, y) in a lateral direction may adopt a function which, for example, has a normal distribution in respect to x, with its standard deviation being dependent upon y.
As a dose is represented by Φ, the formula (6) can be expressed in the following formula (9):
      N    ⁡          (      s      )        =      Φ    ⁢                  ∫                  -          ∞                ∞            ⁢                        n          ⁡                      (                                          s                ⁢                                                                  ⁢                cos                ⁢                                                                  ⁢                θ                            +                              u                ⁢                                                                  ⁢                tan                ⁢                                                                  ⁢                θ                                      )                          ⁢                  g          ⁡                      (                                                            s                  ⁢                                                                          ⁢                  sin                  ⁢                                                                          ⁢                  θ                                -                u                            ,                                                s                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                  θ                                +                                  u                  ⁢                                                                          ⁢                  tan                  ⁢                                                                          ⁢                  θ                                                      )                          ⁢                                  ⁢                  ⅆ          u                    
From this formula (9), an impurity concentration distribution N0(s) at an ion beam incidence angle θ of 0° is given by the following formula (10):
            N      0        ⁡          (      s      )        =                    Φ        ·                  n          ⁡                      (            s            )                              ⁢                        ∫                      -            ∞                    ∞                ⁢                              g            ⁡                          (                                                -                  u                                ,                s                            )                                ⁢                                          ⁢                      ⅆ            u                                =          Φ      ·              n        ⁡                  (          s          )                    
An impurity concentration distribution N(s) can be measured actually by secondary ion mass spectroscopy (SIMS) or the like. It is therefore possible to determine a normalized impurity concentration distribution n(s) in a depth direction.
By setting an ion beam incidence angle to an angle other than 0° to conduct ion implantation in an oblique direction, the impurity concentration distribution N(s) in a depth direction is actually measured by SIMS or the like. Since the shape of the normalized impurity concentration distribution n(s) in a depth direction is determined through measurement of an impurity concentration distribution by ion implantation in a vertical direction, a normalized impurity concentration distribution g(x, y) in a lateral direction can be decided in accordance with the formula (9) and the actually measured impurity concentration distribution N(s).
Spread information of impurities in a lateral direction can be obtained by measuring only the impurity concentration distribution in a depth direction, without directly measuring an impurity concentration distribution in a lateral direction.
The method described above can be adopted only when satisfying the prerequisite that an impurity concentration distribution n(y) in a depth direction by ion implantation in a vertical direction, i.e., along an extension line of an ion beam, is equal to an impurity concentration distribution n(y) on an extension line of an ion beam by ion implantation in an oblique direction.
If a silicon single crystal substrate having a (1 0 0) plane as a principal surface (hereinafter called a (1 0 0) substrate) is used, an ion implantation method at an ion beam incidence angle of 7° is adopted in some cases to suppress the channeling phenomenon. The channeling phenomenon can be suppressed even at an ion beam incidence angle of, e.g., about 25°. It is considered that the normalized impurity concentration distribution n(y) on the extension line of an ion beam at an incidence angle of 25° is approximated to the normalized impurity concentration distribution n(y) along the extension line of an ion beam at an incidence angle of 7°.
At the ion beam incidence angle of 7°, a shift between a propagation direction of an ion beam and a substrate depth direction is extremely small. It is therefore possible to estimate a normalized impurity concentration distribution n(y) on an extension line of an ion beam, from an impurity concentration distribution N(s) in a depth direction at an incidence angle of 7°.
It is therefore possible to evaluate a spread in a lateral direction by actually measuring an impurity concentration distribution in a depth direction at an incidence angle of 7° and an impurity concentration distribution in a depth direction at an incidence angle of 25°. Namely, it is possible to decide a normalized impurity concentration distribution g(x, y) in a lateral direction.
However, if ion implantation into a (1 0 0) substrate is performed at an incidence angle of 0°, the channeling phenomenon is likely to occur. An incidence angle condition does not exist which causes the channeling phenomenon to the same extent as that of the incidence angle of 0°. The method described above cannot evaluate an impurity spread in a lateral direction when ion implantation into a (1 0 0) substrate is performed at an incidence angle of 0°.